Mastering Exponential Variables: How to Solve e^x + e^-x = 4 with Ease

[Chiborino]

My friend just came to me with this problem:
e^x + e^-x = 4
I aced precalc, and I still have no idea where to start on this one. I've factored, natural logged, factored and then natural logged... and I keep running into dead ends.

My graphing calculator puts the answer at +/-1.3169 or something like that.

It's not at all urgent, I'm just curious since I feel that I should know how to solve this problem.

 

[Dick]

If you put u=e^x then e^(-x)=1/u. So it becomes quadratic equation in u. Is that enough of a hint?

 

[Chiborino]

I'm not entirely sure I see how u+1/u can be plugged into the quadratic formula.

Could you please elaborate?

 

[Dick]

u+1/u=4. Multiply both sides by u.

 

[Chiborino]

Oh... I feel kind of dumb now. >_>
Thanks much.